Related papers: When Graph Neural Networks Meet Dynamic Mode Decom…

Graph neural networks (GNNs) demonstrate a robust capability for representation learning on graphs with complex structures, showcasing superior performance in various applications. The majority of existing GNNs employ a graph convolution…

Recent advances in neural algorithmic reasoning with graph neural networks (GNNs) are propped up by the notion of algorithmic alignment. Broadly, a neural network will be better at learning to execute a reasoning task (in terms of sample…

Graph neural networks (GNNs) have emerged as a powerful tool for effectively mining and learning from graph-structured data, with applications spanning numerous domains. However, most research focuses on static graphs, neglecting the…

Functional brain dynamics is supported by parallel and overlapping functional network modes that are associated with specific neural circuits. Decomposing these network modes from fMRI data and finding their temporal characteristics is…

Graphs are essential representations of many real-world data such as social networks. Recent years have witnessed the increasing efforts made to extend the neural network models to graph-structured data. These methods, which are usually…

Graph Neural Networks (GNNs) are an emerging research field. This specialized Deep Neural Network (DNN) architecture is capable of processing graph structured data and bridges the gap between graph processing and Deep Learning (DL). As…

Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the…

Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been…

Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters,…

Dynamic Mode Decomposition (DMD) is a technique to approximate generally non-linear dynamical systems using linear techniques, which are better understood and easier to analyze. Koopman theory extends DMD by transforming the original system…

Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds…

Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is…

Graph neural networks (GNNs) enable the analysis of graphs using deep learning, with promising results in capturing structured information in graphs. This paper focuses on creating a small graph to represent the original graph, so that GNNs…

Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are powerful tools allowing for different kinds of prediction and…

We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…

In recent years, Dynamic Graph (DG) representations have been increasingly used for modeling dynamic systems due to their ability to integrate both topological and temporal information in a compact representation. Dynamic graphs allow to…

Spatiotemporal graph neural networks (STGNNs) have shown promising results in many domains, from forecasting to epidemiology. However, understanding the dynamics learned by these models and explaining their behaviour is significantly more…

Dynamic Graph Neural Networks (GNNs) combine temporal information with GNNs to capture structural, temporal, and contextual relationships in dynamic graphs simultaneously, leading to enhanced performance in various applications. As the…

Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…

This survey paper presents a comprehensive and conceptual overview of anomaly detection using dynamic graphs. We focus on existing graph-based anomaly detection (AD) techniques and their applications to dynamic networks. The contributions…